The title and the subtitle of the book are explained in the author's preface. "The Swerve" refers to a key conception in the ancient atomistic theories according to which atoms moving through the void are subject to clinamen: while falling straight through the void, they are sometimes subject to a slight, unpredictable swerve. Greenblatt uses it to describe the history of Lucretius' own book: "The reappearance of his poem was such a swerve, an unforeseen deviation from the direct trajectory—in this case, toward oblivion—on which that poem and its philosophy seemed to be traveling."[7] The recovery of the ancient text is seen as its rebirth, i.e. a "renaissance". Greenblatt's claim is that it was a 'key moment' in a larger "story.. of how the world swerved in a new direction".[7]

Writing in The New Republic, David Quint saw the book as situated in a controversial tradition that views the Renaissance as a victory of reason over medieval religiosity, following John Addington Symonds, Voltaire and David Hume.[18] Theologian R. R. Reno harshly criticized the book for "blustering again and again about the beauty-loathing, eros-denying evils of Christianity ... sighing in the usual postmodern way about pleasure and desire."[19]

Historian John Monfasani credited the book with "grace and learning" but found Greenblatt's Voltairean and Burckhardtian interpretation of De Rerum Natura and the Renaissance "eccentric", "questionable" and "unwarranted".[20] Greenblatt responded to this critique by reiterating his view of the importance of the Renaissance in history.[21] Several other reviewers criticized Greenblatt's lack of historical rigor and depth while acknowledging some praiseworthy elements. In the Los Angeles Review of Books Jim Hinch saw within the book "two books... one deserving of an award, the other not". He described the first "book" as an "engaging" and "wonderful" exploration of the Renaissance rediscovery of De Rerum Natura, while describing the second book as a far less deserving "anti-religious polemic."[22]

Michael Dirda, of The Washington Post, wrote that "by no means a bad book, The Swerve simply sets its intellectual bar too low, complacently relying on commonplaces in its historical sections and never engaging in an imaginative or idiosyncratic way". Disappointed with the book's simplistic and cliched conclusions, he nonetheless saw Greenblatt’s "excellent notes and bibliography" as a reliable reference for those seeking a more in-depth and serious treatment.[23] Laura Saetveit Miles, of the University of Bergen, criticized the book in explicitly ethical terms, writing that its scholarly and historiographical failings "represent an abuse of power" that "precipitate the decline of the humanities" by lending scholarly authority to the "dire trend of 'truthy' nonfiction books that present One Theory to Explain Everything." She argues that the book is an "injustice to the past" and "the mythical invention of modernity is an ethical issue, because it sets a precedent for history that ignores complexity in favor of oversimplification."[24]

William Caferro of Vanderbilt University found The Swerve "an engaging portrait of the Renaissance sense of wonder and discovery" but was disquieted by the "firm distinction Greenblatt makes between the Renaissance and the Middle Ages" and the lack of reference to current scholarship.[25] Nevertheless he concedes that "if Greenblatt leaves us with more questions than answers, it is ultimately not a grave flaw."[25]